Abstract
In this paper the problem of controllability of a slowly rotating Timoshenko beam in a horizontal plane from the position of rest into an arbitrary position at some given time is investigated. It is solved with the aid of a theorem by D. Ullrich on a trigonometric moment problem which generalizes a classical result of Paley and Wiener.
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References
C. Castro and E. ZĹazĹa, Boundary Controllability of a Hybrid System Consisting in Two Fuxible Beams Connected by a Point Mass. SIAM J. Control Optim. 36(1998), 1576–1595.
W. Krabs and G.M. Sklyar, On the Controllability of a Slowly Rotating Timoshenko Beam. Jornal for Analysis and its Applications 18 (1999), 437–448.
R.E.A.C. Paley and N. Wiener, Fourier Transforms in the Complex Domain. Amer. Math. Soc., Providence, R.J., 1934; 3rd printing 1978.
D Ullrich, Divided Differences and Systems of Norharmonic Fourier Series. Proc. Amer. Soc. 80(1980), 47–57.
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© 2001 Birkhãuser Verlag Basel/Switzerland
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Korobov, V.I., Krabs, W., Sklyar, G.M. (2001). On the Solvability of Trigonometric Moment Problems Arising in the Problem of Controllability of Rotating Beams. In: Hoffmann, KH., Lasiecka, I., Leugering, G., Sprekels, J., Tröltzsch, F. (eds) Optimal Control of Complex Structures. ISNM International Series of Numerical Mathematics, vol 139. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8148-7_12
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DOI: https://doi.org/10.1007/978-3-0348-8148-7_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9456-2
Online ISBN: 978-3-0348-8148-7
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